Centrifugal Convection in Rapid Rotation of Bodies Made of Cellular-Porous Materials

Gas flows inside and around rapidly rotating bodies made of cellular-porous materials are studied numerically and experimentally. Within the framework of the previously proposed physicomathematical model, an appropriate numerical algorithm is developed and tested. Internal flows and a conjugate problem with the external flow are considered. The calculated moment and dynamic pressure are in good agreement with experimentally measured characteristics of a rotating porous disk on a solid substrate. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 46–57, January–February, 2006.     

Some features of the flow around rapidly rotating bodies made of cellular-porous materials

Two types of gas flows arising near a rapidly rotating cellular-porous disk are studied numerically and experimentally. Steady-state limits for the flow around a disk rotating in free space and the type and scenario of the loss of stability are determined. Transitional flows are characterized by formation of a vortex sheet at the boundary of the exhausting jet. Numerical simulations of the flow around a cellular-porous disk rotating near a flat screen show that it is possible to form a closed swirl flow responsible for redistribution of swirl in the gap between the disk and the flat screen. The computed results offer an explanation for the experimentally observed excess of tangential velocity of the flow in the gap over the velocity of disk rotation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 86–96, January–February, 2007.     

Ideal incompressible flow around a wedge tip

A planar analog of conical flows is considered: an inviscid incompressible fluid flow around a wedge tip. A class of conical flows is found where vorticity is transported along streamlines by the potential component of velocity. Problems of a wave “locked” in the corner region and of a flow accelerating along the rib of a dihedral angle are considered. By analogy with an axisymmetric quasi-conical flow, a planar quasi-conical flow of the fluid is determined, namely, the flow inside and outside the region bounded by tangent curves described by a power law. Conditions are found where vorticity and swirl produce a significant effect. An approximate solution of the problem of the fluid flow inside a “zero” angle is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 57–65, March–April, 2007.     

Structure of the long-range fields of plane symmetrical subsonic flows

Plane subsonic potential flows near finite and semi-infinite bodies, symmetrical about thex axis directed along the velocity of the incident flow, are considered. The shape of the isolines of the velocity modulus and the angle of velocity vector inclination to the symmetry axis at large distances from the bodies is found. Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 132–144, May–June, 2000. The work was financially supported by the Russian Foundation for Basic Research (project No. 99-01-00169).     

Investigation of transonic and supersonic flow past a pair of bodies

Transonic and supersonic flows past a pair of bodies have been experimentally investigated. The leading bodies were spheres, cylinders, and cones, while the trailing bodies were flat-ended circular cylinders. The leading and trailing bodies were joined by cylindrical rods of various lengths, aligned with the axis of symmetry. For these models, the pattern of flow between the bodies and the Mach number dependence of the drag coefficientC _x were determined in the acceleration and deceleration flow regimes in a wind tunnel. The experimental results are used to analyze the properties of the flow between the bodies and the variation of the aerodynamic coefficients of the models. The reasons for the hysteresis in the behavior of the coefficients in the acceleration and deceleration stages are discussed. The influence of the shape and dimensions of the leading body on the modelC _x is evaluated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 158–164, March–April, 1998.     

Galilean-invariant axisymmetric self-similar submodel of gas dynamics without swirling

This paper deals with one insufficiently studied submodel of invariant solutions of rank 1 of the equations of gas dynamics. It is shown that, in cylindrical coordinates, the submodel without swirling reduces to a system of two ordinary differential equations. For the equation of state with additional invariance, a self-similar system is obtained. A pattern of phase trajectories is constructed, and particle motion is studied using asymptotic methods. The obtained solutions describe unsteady flows over axisymmetric bodies with possible strong discontinuities. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 46–52, March–April, 2009.     

Modeling of fluid dynamics interacting with ductile fraction propagation in high pressure pipeline

This paper presents a computational model for the fluid dynamics in a fractured ductile pipe under high pressure. The pressure profile in front of the crack tip, which is the driving source of crack propagation, is computed using a nonlinear wave equation. The solution is coupled with a one dimensional choked flow analysis behind the crack. The simulation utilizes a high order optimized prefactored compact-finite volume method in space, and low dispersion and dissipation Runge-Kutta in time. As the pipe fractures the rapid depressurization take place inside the pipe and the propagation of the crack-induced waves strongly influences the outflow dynamics. Consistent with the experimental observation, the model predicts the expansion wave inside the pipe, and the reflection and outflow of the wave. The model also helps characterize the propagation of the crack dynamics and fluid flows around the tip of the crack.     

Modeling the motion of a vapor bubble in a tube in an ascending flow

The steady rise of a vapor bubble in a liquid moving in a vertical tube is modeled by means of the Navier-Stokes equations. The shape of the vapor bubble (drop) and the structure of the flow are determined by numerically solving the equations inside and outside the drop. The calculations are made on the interval of intermediate values of the dimensionless parameters and describe the transition to piston-type motion. The solutions obtained are compared with the existing experimental and approximate data for creeping flows. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 76–86, July–August, 1994.     

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.     

Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Prediction of separation flows around a 6：1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows. The project supported by the National Natural Science Foundation of China (10502030 and 90505005).     

Possibilities and Limitations of Computer Simulations of Industrial Turbulent Dispersed Multiphase Flows

We give an overview on the usage of computer simulations in industrial turbulent dispersed multiphase flows. We present a few examples of industrial flows: bubble columns and bubbly pipe flows, stirred tanks, cyclones, and a fluid catalytic cracking unit. The fluid catalytic cracking unit is used to illustrate the complexity of the physical phenomena involved, and the possibilities and limitations of the different approaches used: Eulerian–Lagrangian (particle-tracking) and Eulerian–Eulerian (two-fluid). In the first approach, the continuous phase is solved using either RANS simulations (Reynolds-Averaged Navier–Stokes simulations) or DNS/LES (Direct Numerical Simulations/Large-Eddy Simulations), and the individual particles are tracked. In the second approach, the dispersed phase is averaged, leading to two sets equations, which are quite similar to the RANS equations of single-phase flows. The Eulerian–Eulerian approach is the most commonly used in industrial applications, however, it requires a significant amount of modelling. Eulerian–Lagrangian RANS can be simpler to use; in particular in situations involving complex boundary conditions, polydisperse flows and agglomeration/breakup. The key issue for the success of the simulations is to have good models for the complex physics involved. A major weakness is the lack of good models for: the turbulence modification promoted by the particles, the inter-particle interactions, and the near-wall effects. Eulerian–Lagrangian DNS/LES can play an important role as a research tool, in order to get a better physical understanding, and to improve the models used in the RANS simulations (either Eulerian–Eulerian or Eulerian–Lagrangian).     

Turbulence kinetic energy budget in bubbly flows in a vertical duct

Understanding turbulence kinetic energy (TKE) budget in gas–liquid two-phase bubbly flows is indispensable to develop and improve turbulence models for the bubbly flows. In this study, a molecular tagging velocimetry based on photobleaching reaction was applied to turbulent bubbly flows with sub-millimeter bubbles in a vertical square duct to examine the applicability of the k–ε models to the bubbly flows. Effects of bubbles on TKE budget are discussed and a priori tests of the standard and low Reynolds number k–ε models are carried out to examine the applicability of these models to the bubbly flows. The conclusions obtained are as follows: (1) The photobleaching molecular tagging velocimetry is of use for validating turbulence models. (2) The bubbles increase the liquid velocity gradient in the near wall region, and therefore, enhance the production and dissipation rates of TKE. (3) The k–ε models can reasonably evaluate the production rate of TKE in the bubbly flows. (4) The modulations of diffusion due to the bubbles have different characteristics from the diffusion enhancement due to shear-induced turbulence. Hence, the k–ε models fail in evaluating the diffusion rate in the near wall region in the bubbly flows. (5) The k–ε models represent the trends of the production, dissipation, and diffusion rates of ε in the bubbly flow, although more accurate experimental data are required for quantitative validation of the ε equation.     

Stabilization of the Rotation Axis of a Solid by Coupled Perfectly Rigid Bodies

The problem of stabilizing the axis of a solid by coupled perfectly rigid bodies (PRBs) is solved. The solid executes a plane-parallel motion. The PRBs can rotate as a single rigid body about the centroidal axis of the solid and counterrotate about its transverse axes through equal angles. There is a particle inside the solid which causes its imbalance. It is established that the principal state (if any) of the system—rotation about the centroidal axis—is stable, whereas the rest (unwanted) states are unstable __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 122–129, August 2005.     

Three-Dimensional Instability of Planar Flows

We study the stability of two-dimensional solutions of the three-dimensional Navier–Stokes equations, in the limit of small viscosity. We are interested in steady flows with locally closed streamlines. We consider the so-called elliptic and centrifugal instabilities, which correspond to the continuous spectrum of the underlying linearized Euler operator. Through the justification of highly oscillating Wentzel–Kramers–Brillouin expansions, we prove the nonlinear instability of such flows. The main difficulty is the control of nonoscillating and nonlocal perturbations issued from quadratic interactions.     

Physical and mathematical modeling of a supersonic flow around a cylinder with a porous insert

Results of numerical and experimental modeling of a supersonic flow (M_∞ = 4.85) around a model of a streamwise-aligned cylinder with a cellular-porous insert permeable for the gas on the frontal face of the cylinder are described. Experimental data on the influence of the pore structure and the length of the porous cylindrical insert on the model drag, pressure on the frontal face of the cylinder, and flow pattern are obtained. Numerical modeling includes solving Favre-averaged Navier-Stokes equations, which describe the motion of a viscous compressible heat-conducting gas. The system is supplemented with a source term taking into account the drag of the porous body within the framework of the continuum model of filtration. Data on pressure and velocity fields inside the porous body are obtained in calculations, and the shape of an effective pointed body whose drag is equal to the drag of the model considered is determined. The calculated results are compared with the measured data and schlieren visualization of the flow field.     

Calculation of stagnation streamline quantities in hypersonic blunt body flows

An approximate method for the efficient calculation of stagnation-streamline quantities in hypersonic flows about spheres or cylinders is suggested. Based on the local similarity of the flow field the two-dimensional Navier-Stokes equations are simplified to a one-dimensional approximation for the stagnation streamline. These equations are solved with an implicit finite-volume scheme. Comparisons with fully two–dimensional Euler and Navier–Stokes calculations for flows about spheres are presented, that include perfect gas flows and flows in chemical non-equilibrium. Comparisons with a number of experiments conclude this report. Received 8 May 1996 / Accepted 31 October 1996     

Interaction of shear flows of an ideal incompressible fluid in a channel

The problem of the decay of an arbitrary discontinuity for the equations describing plane-parallel shear flows of an ideal fluid in a narrow channel is considered. The class of particular solutions corresponding to fluid flows with piecewise constant vorticity is studied. In this class, the existence of self-similar solutions describing all possible unsteady wave configurations resulting from the nonlinear interaction of the specified shear flows is established. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 34–47, November–December, 2006.     

Strong discontinuities in spatial stationary long-wave flows of an ideal incompressible fluid

Spatial stationary flows over an even bottom of a heavy ideal fluid with a free surface are considered. Jump relations for flows with a strong discontinuity are studied. It is shown that the flow parameters behind the jump are defined by a certain curve which is an analog of the (θ, p) diagram in gas dynamics. A shock polar and examples of flows with a hydraulic jump are constructed for a particular class of solutions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 37–45, March–April, 2009.     

Macroscopic description of steady and unsteady rarefaction effects in boundary value problems of gas dynamics

Four basic flow configurations are employed to investigate steady and unsteady rarefaction effects in monatomic ideal gas flows. Internal and external flows in planar geometry, namely, viscous slip (Kramer’s problem), thermal creep, oscillatory Couette, and pulsating Poiseuille flows are considered. A characteristic feature of the selected problems is the formation of the Knudsen boundary layers, where non-Newtonian stress and non-Fourier heat conduction exist. The linearized Navier–Stokes–Fourier and regularized 13-moment equations are utilized to analytically represent the rarefaction effects in these boundary-value problems. It is shown that the regularized 13-moment system correctly estimates the structure of Knudsen layers, compared to the linearized Boltzmann equation data.